Question 540781
You know that the ratios of side lengths are 3/4 or 4/3 for both kites.
If the bigger kite's side with a measure of 7 is the longer side, like this
{{{drawing( 400, 300, -10, 10, -10, 10,
  locate( -4.9, 2.2, 3 ), locate( -7.5, 2.2, 3 ),
  locate( -4.9, -1.5, 4 ), locate( -7.5, -1.5, 4 ),
  locate( 1.5, -3.5, 7 ), locate( 6.1, -3.5, 7 ),
  locate( 1.5, 4.4, x ), locate( 6.1, 4.4, x ),
  line( -4, 0, -6, 3 ),
  line( -4, 0, -6, -4 ),
  line( -8, 0, -6, 3 ),
  line(-8, 0, -6, -4),
  line( 0, 0, 4, 6 ),
  line( 0, 0, 4, -8 ),
  line( 8, 0, 4, 6 ),
  line( 8, 0, 4, -8)
  )}}}then {{{3/4=x/7}}} --> {{{x=21/4=5.25}}}
If the bigger kite's side with a measure of 7 is the shorter side, like this
{{{drawing( 400, 300, -10, 10, -10, 10,
  locate( -4.9, 2.2, 3 ), locate( -7.5, 2.2, 3 ),
  locate( -4.9, -1.5, 4 ), locate( -7.5, -1.5, 4 ),
  locate( 1.5, -3.5, x ), locate( 6.1, -3.5, x ),
  locate( 1.5, 4.4, 7 ), locate( 6.1, 4.4, 7 ),
  line( -4, 0, -6, 3 ),
  line( -4, 0, -6, -4 ),
  line( -8, 0, -6, 3 ),
  line(-8, 0, -6, -4),
  line( 0, 0, 4, 6 ),
  line( 0, 0, 4, -8 ),
  line( 8, 0, 4, 6 ),
  line( 8, 0, 4, -8)
  )}}}then {{{4/3=x/7}}} --> {{{x=28/3}}} (approximately 9.33)
If the problem does not tell which side has a length of 7, then there are 2 possible answers.